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Pre-Calculus Course Outline

The first semester of Pre-calculus explores trig functions and sinusoids. The second semester examines a variety of topics from analytic geometry to probability to polar coordinates and complex numbers. The course should also contain review of earlier algebraic concepts. This course uses Pre-Calculus by P. Foerster.

Chapter 1: Functions and Mathematical Models

  • dilations, translations, and transformations
  • composition of functions
  • inverses of functions
  • reflections and absolute values

Chapter 2: Periodic Functions and Right Triangle Problems

  • periodic functions
  • measurements of rotation
  • trig functions
  • inverse trig functions

Chapter 3: Applications of Trigonometric and Circular Functions

  • sinusoids
  • amplitudes, period, and cycles
  • radians
  • circular functions

Chapter 4: Trigonometric Functions, Properties, Identities, and Parametric Functions

  • the Pythagorean property
  • trig identities
  • arcsines, arccosines, and arctangents
  • inverse trig relations

Chapter 5: Properties of Combined Sinusoids

  • combination of sinusoids
  • composition argument properties
  • sum and product properties
  • double and half argument properties

Chapter 6: Triangle Trigonometry

  • oblique triangles
  • law of sines and law of cosines
  • area of triangles
  • vectors
  • triangle problems

Chapter 7: Properties of Elementary Functions

  • shapes of functions
  • graphical patterns
  • numerical patterns
  • properties of logarithms
  • logarithmic functions
  • logistic functions for growth

Chapter 8: Fitting Functions to Data

  • regression equations
  • correlations
  • regression for nonlinear data
  • residual plots

Chapter 9: Probability and Functions of Random Variability

  • principles of probability
  • counting principles
  • permutations and combinations
  • functions of a random variable
  • mathematical expectation

Chapter 12: Analytic Geometry of Conic Selections and Quadratic Surfaces

  • conic sections
  • parametric equations of conics
  • analytic geometry
  • application of conics

Chapter 13: Polar Coordinates, Complex Numbers, and Moving Objects

  • polar coordinates
  • polar equations of conics and other curves
  • intersection of polar coordinates
  • complex numbers in complex form

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